Rectangle Diagonal Calculator
Enter the rectangle length and width to instantly calculate the diagonal using the Pythagorean theorem.
How to find the diagonal of a rectangle
The diagonal of a rectangle is the straight line connecting one corner to the opposite corner. If you know the rectangle’s length and width, you can calculate the diagonal quickly and accurately.
This is one of the most common geometry calculations in school math, construction, design, and DIY projects. Whether you are sizing a TV, planning a room layout, or checking a frame dimension, this calculator saves time and helps reduce mistakes.
d = √(l² + w²)
d = diagonal, l = length, w = width
Why this formula works
A rectangle creates a right triangle when you draw its diagonal. The length and width are the two legs of that triangle, and the diagonal is the hypotenuse. The Pythagorean theorem states:
hypotenuse² = leg₁² + leg₂²
So for a rectangle, that becomes d² = l² + w², and taking the square root gives d = √(l² + w²).
Step-by-step example
Suppose your rectangle has:
- Length = 12 cm
- Width = 5 cm
Then:
- 12² = 144
- 5² = 25
- 144 + 25 = 169
- √169 = 13
Diagonal = 13 cm
When this calculator is useful
- Home improvement: measuring corner-to-corner distances for flooring, wall panels, or fixtures.
- Screen sizes: estimating monitor or TV dimensions from width and height.
- Furniture planning: checking if an item fits through a hallway or doorway at an angle.
- Engineering and drafting: quick checks of rectangular parts and CAD dimensions.
- Education: geometry practice and homework verification.
Common mistakes to avoid
1) Mixing units
If length is in inches and width is in centimeters, convert them first so both inputs use the same unit.
2) Forgetting to square both sides
Both length and width must be squared before adding.
3) Rounding too early
Keep full precision until the final answer for better accuracy, especially in professional measurements.
4) Using negative values
Dimensions represent distances, so they should always be positive.
Quick reference values
| Length | Width | Diagonal |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 9 | 12 | 15 |
Frequently asked questions
Is rectangle diagonal the same as hypotenuse?
In the right triangle formed by the rectangle’s length, width, and diagonal, yes—the diagonal is the hypotenuse.
Can I use decimal values?
Absolutely. This calculator supports whole numbers and decimals.
Does orientation matter?
No. Swapping length and width gives the same diagonal because both values are squared.
Can I use this for squares?
Yes. A square is a special rectangle where length and width are equal.
Final thoughts
The diagonal of a rectangle calculator is a simple but practical tool. By combining two measurements and one formula, you can quickly find corner-to-corner distance for planning, building, and learning. Enter your values above to get an instant result with area and perimeter as bonus outputs.